Finite Group Databasebeta

← #26028463

Subgroups — #26028463

Order 11392.

400 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19151538C211yesmaximal, characteristic, complemented
2#19151533C211yesmaximal, characteristic, complemented
3#19151533C211yesmaximal, characteristic, complemented
4#19151529C211yesmaximal, characteristic, complemented
5#19151527C211yesmaximal, characteristic, complemented
6#19151527C211yesmaximal, characteristic, complemented
7#19151522C211yesmaximal, characteristic, complemented
8#19151520C211yesmaximal, characteristic, complemented
9#19151516C211yesmaximal, characteristic
10#19151515C211yesmaximal, characteristic
11#19151515C211yesmaximal, characteristic
12#19151493C211yesmaximal, characteristic, complemented
13#19151490C211yesmaximal, characteristic, complemented
14#19151488C211yesmaximal, characteristic, complemented
15#398×C89C211yesmaximal, characteristic, complemented
16C22×D356C2211yescharacteristic
17C2×C4⋊Dic89C2211yescharacteristic
18C2×#13083553C2211yescharacteristic
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2211yescharacteristic
23C2×#13083553C2211yescharacteristic
24C2×#13083551C2211yescharacteristic
25C2×#13083551C2211yescharacteristic
26C2×#13083551C2211yescharacteristic
27C2×#13083551C2211yescharacteristic
28C2×#13083551C2211yescharacteristic
29C2×#13083551C2211yescharacteristic
30C2×#13083551C2211yescharacteristic
31C2×#13083551C2211yescharacteristic
32C2×#13083551C2211yescharacteristic
33C2×#13083551C2211yescharacteristic
34C2×#13083551C2211yescharacteristic
35C2×#13083551C2211yescharacteristic
36C2×C4×Dic89C2211yescharacteristic
37#15667919C2211yescharacteristic
38#15667919C2211yescharacteristic
39#15667919C2211yescharacteristic
40#15667919C2211yescharacteristic
41#15667919C2211yescharacteristic
42#15667919C2211yescharacteristic
43#15667919C2211yescharacteristic
44C2×C4⋊C4×C89C2211yescharacteristic
45C2×C4⋊C4×C89C2211yescharacteristic
46C2×C4⋊C4×C89C2211yescharacteristic
47C2×C4⋊C4×C89C2211yescharacteristic
48#95×C89C2211yescharacteristic
49#95×C89C2211yescharacteristic
50#95×C89C2211yescharacteristic
51C23×D89C2311yescharacteristic
52C23×D89C2311yescharacteristic
53C2×D356—41no—
54C2×D356—41no—
55C2×D356—41no—
56C22×Dic89C2311yescharacteristic
57C22×Dic89C2311yescharacteristic
58C22×Dic89C2311yescharacteristic
59C22×Dic89C2311yescharacteristic
60C22×Dic89C2311yescharacteristic
61C22×Dic89C2311yescharacteristic
62C4⋊Dic89—41no—
63#13083553—22no—
64#13083553—41no—
65#13083553—41no—
66#13083553—41no—
67#13083553—41no—
68#13083553—41no—
69#13083551—22no—
70#13083551—22no—
71#13083551—41no—
72#13083551—41no—
73#13083551—41no—
74#13083551—41no—
75#13083551—41no—
76#13083551—41no—
77#13083551—41no—
78#13083551—41no—
79#13083551—41no—
80#13083551—41no—
81C4×Dic89—41no—
82C22×C4×C89C2311yescharacteristic
83C22×C4×C89C2311yescharacteristic
84C22×C4×C89C2311yescharacteristic
85C22×C4×C89C2311yescharacteristic
86C22×C4×C89C2311yescharacteristic
87C22×C4×C89C2311yescharacteristic
88C22×C4×C89C2311yescharacteristic
89C4⋊C4×C89—41no—
90C4⋊C4×C89—41no—
91C4⋊C4×C89—41no—
92C4⋊C4×C89—41no—
93C23×C89C2411yescharacteristic
94C22×D89—21no—
95C22×D89—21no—
96C22×D89—21no—
97C22×D89—21no—
98C22×D89—21no—
99C22×D89—21no—
100C22×D89—21no—
101C22×D89—21no—
102C22×D89—21no—
103C22×D89—21no—
104C22×D89—21no—
105C22×D89—21no—
106C22×D89—21no—
107C22×D89—21no—
108C2×C4×C89—21no—
109C2×C4×C89—21no—
110C2×C4×C89—21no—
111C2×C4×C89—21no—
112C2×C4×C89—21no—
113C2×C4×C89—21no—
114C2×C4×C89—21no—
115C2×C4×C89—21no—
116C2×C4×C89—21no—
117C2×C4×C89—21no—
118C2×C4×C89—21no—
119C2×C4×C89—21no—
120C2×C4×C89—21no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×Dic89—21no—
130C2×Dic89—21no—
131C2×Dic89—21no—
132C2×Dic89—21no—
133C2×Dic89—21no—
134C2×Dic89—21no—
135C2×Dic89—21no—
136C2×Dic89—21no—
137C2×Dic89—21no—
138C2×Dic89—21no—
139C2×Dic89—21no—
140C2×Dic89—21no—
141C2×Dic89—21no—
142C2×Dic89—21no—
143C2×Dic89—21no—
144C2×Dic89—21no—
145C2×Dic89—21no—
146C2×Dic89#4112yes—
147D356—44no—
148C22×C89C2×#4111yescharacteristic
149C22×C89H(5,𝔽2)11yescharacteristic
150C22×C89H(5,𝔽2)11yescharacteristic
151C22×C89H(5,𝔽2)11yescharacteristic
152C22×C89H(5,𝔽2)11yescharacteristic
153C22×C892−1+411yescharacteristic
154C22×C892−1+411yescharacteristic
155C2×D89—41no—
156C2×D89—41no—
157C2×D89—41no—
158C2×D89—41no—
159C2×D89—41no—
160C2×D89—41no—
161C2×D89—41no—
162C2×D89—41no—
163C2×D89—41no—
164C2×D89—41no—
165C2×D89—41no—
166C2×D89—41no—
167C2×D89—41no—
168C2×D89—41no—
169C4×C89—41no—
170C4×C89—41no—
171C4×C89—41no—
172C4×C89—41no—
173C4×C89—41no—
174C4×C89—41no—
175C4×C89—41no—
176Dic89—22no—
177Dic89—41no—
178Dic89—41no—
179Dic89—41no—
180Dic89—41no—
181Dic89—41no—
182C2×C89#53911yescharacteristic
183C2×C89#54011yescharacteristic
184C2×C89#54211yescharacteristic
185C2×C89#56011yescharacteristic
186C2×C89#56211yescharacteristic
187C2×C89#56211yescharacteristic
188C2×C89#56311yescharacteristic
189D89—81no—
190D89—81no—
191#2837—891nomaximal, Sylow
192C89#283711yescharacteristic, complemented, Sylow
193#400—891no—
194#399—891no—
195#399—891no—
196#398—891no—
197#398D8911yescharacteristic, complemented
198#397—891no—
199#397—891no—
200#396—891no—
201#396—891no—
202#394—891no—
203#394—891no—
204#394—891no—
205#389—891no—
206#388—891no—
207#388—891no—
208C22×D4—891no—
209C2×C4⋊C4—891no—
210C2×C4⋊C4—891no—
211C2×C4⋊C4—891no—
212C2×C4⋊C4—891no—
213C2×C4⋊C4—891no—
214C2×C4⋊C4—891no—
215C2×C4⋊C4—891no—
216C2×C4⋊C4C2×D8911yescharacteristic
217C2×C4⋊C4C2×D8911yescharacteristic
218C2×C4⋊C4C2×D8911yescharacteristic
219C2×C4⋊C4C2×D8911yescharacteristic
220C2×C22⋊C4—891no—
221C2×C22⋊C4—891no—
222C2×C22⋊C4—891no—
223C2×C22⋊C4—891no—
224C2×C22⋊C4—891no—
225C2×C22⋊C4—891no—
226C2×C22⋊C4—891no—
227C2×C22⋊C4—891no—
228C2×C22⋊C4—891no—
229C2×C22⋊C4—891no—
230C2×C22⋊C4—891no—
231C2×C22⋊C4—891no—
232C2×C42—891no—
233#95—891no—
234#95—891no—
235#95—891no—
236#95—891no—
237#95—891no—
238#95—891no—
239#95—891no—
240#95C2×D8911yescharacteristic
241#95C2×D8911yescharacteristic
242#95C2×D8911yescharacteristic
243C24—891no—
244C24—891no—
245C2×D4—3561no—
246C2×D4—3561no—
247C2×D4—3561no—
248C22×C4—891no—
249C22×C4—891no—
250C22×C4—891no—
251C22×C4—891no—
252C22×C4—891no—
253C22×C4—891no—
254C22×C4C22×D8911yescharacteristic
255C22×C4C22×D8911yescharacteristic
256C22×C4C22×D8911yescharacteristic
257C22×C4C22×D8911yescharacteristic
258C22×C4C22×D8911yescharacteristic
259C22×C4C22×D8911yescharacteristic
260C22×C4C22×D8911yescharacteristic
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—3561no—
266C4⋊C4—3561no—
267C4⋊C4—3561no—
268C4⋊C4—3561no—
269C4⋊C4—3561no—
270C4⋊C4—3561no—
271C4⋊C4—1782no—
272C22⋊C4—3561no—
273C22⋊C4—3561no—
274C22⋊C4—3561no—
275C22⋊C4—3561no—
276C22⋊C4—3561no—
277C22⋊C4—3561no—
278C22⋊C4—3561no—
279C22⋊C4—3561no—
280C22⋊C4—3561no—
281C22⋊C4—3561no—
282C22⋊C4—1782no—
283C22⋊C4—1782no—
284C42—3561no—
285C23—1781no—
286C23—1781no—
287C23—1781no—
288C23—1781no—
289C23—1781no—
290C23—1781no—
291C23—1781no—
292C23—1781no—
293C23—1781no—
294C23—1781no—
295C23—1781no—
296C23—1781no—
297C23—1781no—
298C23—1781no—
299C23C23×D8911yescharacteristic
300D4—3564no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—892no—
323C2×C4—1781no—
324C2×C4—1781no—
325C2×C4—1781no—
326C2×C4—1781no—
327C2×C4—1781no—
328C2×C4—1781no—
329C2×C4—1781no—
330C2×C4—1781no—
331C2×C4—1781no—
332C2×C4—1781no—
333C2×C4—1781no—
334C2×C4—1781no—
335C2×C4—1781no—
336C2×C4—1781no—
337C2×C4—1781no—
338C2×C4—1781no—
339C2×C4—1781no—
340C22—3561no—
341C22—3561no—
342C22—3561no—
343C22—3561no—
344C22—3561no—
345C22—3561no—
346C22—3561no—
347C22—3561no—
348C22—3561no—
349C22—3561no—
350C22—3561no—
351C22—3561no—
352C22—3561no—
353C22—3561no—
354C22#41×D8911yescharacteristic
355C22#1566805711yescharacteristic
356C22#1566805711yescharacteristic
357C22#1566805811yescharacteristic
358C22#1566805811yescharacteristic
359C22#1566806011yescharacteristic
360C22#1566806011yescharacteristic
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3561no—
369C4—3561no—
370C4—3561no—
371C4—3561no—
372C4—3561no—
373C4—1782no—
374C2—7121no—
375C2—7121no—
376C2#1915219611yescharacteristic
377C2#1915220011yescharacteristic
378C2#1915221811yescharacteristic
379C2#1915233611yescharacteristic
380C2#1915234411yescharacteristic
381C2#1915234611yescharacteristic
382C2#1915234711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC22×D356C22
hypercenter#398D89
hypocenterC89#2837
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19151538C2semidirect
2. #19151533C2semidirect
3. #19151533C2semidirect
4. #19151529C2semidirect
5. #19151527C2semidirect
6. #19151527C2semidirect
7. #19151522C2semidirect
8. #19151520C2semidirect
12. #19151493C2semidirect
13. #19151490C2semidirect
14. #19151488C2semidirect
15. #398×C89C2semidirect
192. C89#2837semidirect
197. #398D89semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191515382
#191515332
#191515292
#191515272
#191515222
#191515202
#191515162
#191515152
#191514932
#191514902
#191514882
#398×C892
#283789